02-8 - Hinge Moments

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FLIGHT DYNAMICS & STABILITY

Lecture 02-8: Hinge Moments

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Hinge Moment

The aerodynamic forces on any control surface produce a

moment about the hinge known as the hinge moment

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Effect of Hinge Moment

The force that the control system must exert to hold

the elevator at the desired angle is in direct proportion

to the hinge moment

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Hinge Moment Coefficient

The hinge moment is roughly proportional to the square of

speed and cube of the airplane size

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Normal Force Distribution

Two-dimensional airfoil theory shows that the hinge

moment of simple flap controls is linear with angle of attack

and control angle in both subsonic and supersonic flow

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Elevator and Tab Deflection

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Trim Tab

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Hinge Moment Coefficient

• The hinge moment parameters are very difficult

to predict analytically with great precision

• Wind tunnel tests are usually required

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Free Elevator

• A characteristic of interest is the stability of theairplane when the elevator is set free

• It is completely free to rotate about its hinge under theinfluence of the aerodynamic pressures that act upon it

• Normally, the stability in the control-free condition isless than with fixed controls

• It is desirable that this difference should be small• Since friction is always present in the control system,

the free control is never realized in practice. However,the two ideal conditions, free control and fixed control,represent the possible extremes.

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Stick-Free Longitudinal Stability

•Let us assume that the elevator is mounted on a frictionlesshinge so that it can float freely under the action of

aerodynamic forces when allowed to do so.

• The elevator will either float up or down depending on

location of the hinge-line relative to its center of pressure.

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Elevator Floating Characteristics

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Elevator Floating angle

Assuming that both  and  are equal to zero:

Usually,  and

 are negative

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Tail Lift Coeff. with Free Elevator

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=

where    = 1

=

∴ = 1 ℎ

ℎ

: Flap Effectiveness

ParameterBut

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Stick-Fixed Case

=

+ +

+  

=

+

1

Stick-Free Case

′ = +

+

′ +  

′ =

+

′ 1

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Neutral Point

=

+

1

′

=

+

′

1

Stick-Fixed:

Stick-Free:

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Difference between NPs

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where    = 1

=

ℎ

ℎ

1

′

= 1

1

∴ 

 ′

=

ℎ

ℎ

1

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Static Margins

= − =

=

−

′

= − =

=

−

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Example 1

Obtain the shift in the neutral point for an airplane if the values of some of it’s

parameters are: = 0.738, = 0.9, = 4.17 −,

= 3.43 −,

/ = 0.438. Assume τ = 0.5, ℎ= 0.005 −, ℎ

= 0.003 −.

∴ = 1 ℎ

ℎ

= 1 0 . 5 ∗0.003

0.005= 0.7 

′

= 1

1  

= 1 0.7 ∗ 0.738 ∗ 0.9 ∗3.43

4.171 0.438 = 0.0921 

Solution:

By freeing the stick, the neutral point has shifted forward by .   or the static

margin has decreased by 0.0921. In other words,

′ = 0.0921 .

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Example 2

An airplane has the following characteristics:

= 0.085 −, = 0.058 −, / = 0.032,

ℎ= 0.003 −, ℎ

= 0.0055 −, = 0, = 2 ,   = 1,

= 0.5 , = 0.25 , = 3, / = 1500 /, . . = 0.25,

  = 1.0, ,,= 0.37 − 

Obtain

i) Stick-fixed neutral point.

ii) Stick-free neutral point.

iii) Stick -free neutral point when is changed to 0.003.

Solution:

= 0.5, =

= 0.25 ∗ 3 = 0.75 

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Stick-Fixed Neutral Point:

=

,,

+

1

= 0.25 0.37

4.87+ 1.0 ∗ 0.75 ∗

3.323

4.871 0.5 = 0.4301 

Stick-Free Neutral Point:

′

=

,,

+

1

1

ℎ

ℎ

= 0.25 0.37

4.87+ 1.0 ∗ 0.75 ∗

3.323

4.871 0.5 1

0.032

0.058∗

0.003

0.0055 

= 0.355 

Stick-Free Neutral Point (when ℎ= 0.003):

= 0.25 0.37

4.87+ 1.0 ∗ 0.75 ∗

3.323

4.871 0.5 1

0.032

0.058∗

+0.003

0.0055 

= 0.5051 

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Trim Tabs

• Small surfaces called trim tabs are connected tothe trailing edge of a bigger control surface on anairplane such as its rudder, elevators, or ailerons.

• The trim tabs counter aerodynamic forces andstabilize the airplane in a desired positionwithout having the operator continually apply a

control force to the particular control surface.

• This action is made by adjusting the angle of thetrim tab in relation to the larger control surface.

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Trim Wheel

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Trim with Trim Tab

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Trim Condition

• In order to fly at a given speed, or C L , it has been

shown that a certain elevator angle is required

•  When this differs from the free-floating angle a

force is required to hold the elevator

• When flying for long periods at a constant speed,

it is very fatiguing for the pilot to maintain such aforce

• The trim tabs are used to relieve the pilot of this

load by causing  and  to coincide